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Delay Difference Equations and Their Applications
Jánský, Jiří ; Hilscher, Roman Šimon (oponent) ; Čermák, Libor (oponent) ; Čermák, Jan (vedoucí práce)
This thesis discusses the qualitative properties of some delay difference equations. These equations originate from the $\Theta$-method discretizations of the differential equations with a delayed argument. Our purpose is to analyse the asymptotic properties of these numerical solutions and formulate their upper bounds. We also discuss stability properties of the studied discretizations. Several illustrating examples and comparisons with the known results are presented as well.
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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
This thesis is a review of Delay Differential Equations in Dynamical systems. Starting with a general overview of Delay Differential Equations, we present the concept on Delay Differentials and the application of its models, ranging from biology and population dynamics to physics and engineering. We will also give an overview on Dynamical systems and delay differential equations in the dynamic systems .An area for modelling with delay differentials equations is Epidemiology. Emphasis is given to the development of the Susceptible-Infected-Removed(SIR) epidemiological model without and with time delay. We the analyse our two models under equilibra and local stability using assumed data of COVID -19 .Results would be compared between the model without delays and model with delays.
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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
This thesis is a review of Delay Differential Equations in Dynamical systems. Starting with a general overview of Delay Differential Equations, we present the concept on Delay Differentials and the application of its models, ranging from biology and population dynamics to physics and engineering. We will also give an overview on Dynamical systems and delay differential equations in the dynamic systems .An area for modelling with delay differentials equations is Epidemiology. Emphasis is given to the development of the Susceptible-Infected-Removed(SIR) epidemiological model without and with time delay. We the analyse our two models under equilibra and local stability using assumed data of COVID -19 .Results would be compared between the model without delays and model with delays.
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Delay Difference Equations and Their Applications
Jánský, Jiří ; Hilscher, Roman Šimon (oponent) ; Čermák, Libor (oponent) ; Čermák, Jan (vedoucí práce)
This thesis discusses the qualitative properties of some delay difference equations. These equations originate from the $\Theta$-method discretizations of the differential equations with a delayed argument. Our purpose is to analyse the asymptotic properties of these numerical solutions and formulate their upper bounds. We also discuss stability properties of the studied discretizations. Several illustrating examples and comparisons with the known results are presented as well.
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